miscellaneous problems in derivatives of trigonometric functions
please help me solve the problems below. As always, I end up with incorrect answers in some items of my reviewer. Here it is: find dy/dx
1.) y= xsinx + (1-1/2 x^2)cosx
Ans: 1/2 x^2 sinx
my ans: -sinx + 1/2 x^2 sinx
2.) y = 1-u/1+u ; u = cos2x
ans: 2tanxsec^2 x
my ans: (4sin2x)/(1+cos2x)^2
3.) x = cosu + usinu ;
y = sinu - ucosu
ans: tanu
my ans: (cosu + usinu)/(-sinu + ucosu)
4.) y = tan(x+y)
ans: -csc^2(x+y) = -(1 + y^-2)
my ans: sec^2(x+y)(1 + dy/dx)
hope you can help me! Thanks in advance. :)